Matmat is playing a card game together with his friends as their activity during their leisure time. He was stuck in a win or lose situation. When he draws a card from the standard deck of cards, what is the probability of getting an odd number that is less than 10, but greater than 3 or a black?

Solution

M a t ma t i s pl a y in g a c a r d g am e t o g e t h er w i t h hi s f r i e n d s a s t h e i r a c t i v i t y d u r in g t h e i r l e i s u re t im e . He w a s s t u c k in a w in or l ose s i t u a t i o n . Wh e n h e d r a w s a c a r d f ro m t h e s t an d a r d d ec k o f c a r d s, w ha t i s t h e p ro babi l i t y o f g e tt in g an o dd n u mb er t ha t i s l ess t han 10, b u t g re a t er t han 3 or a b l a c k ?

\frac{1}{2}

Decimal

0.5

Solution steps

Find the probability of getting odd 10 3 :

0

Find the probability of a black:

\frac{1}{2}

Since the events are disjoint, Use the formula

P (X_{1} \lor X_{2} \lor \dots \lor X_{k}) = P (X_{1}) + P (X_{2}) + \dots + P (X_{k})

= 0 + \frac{1}{2}

Apply rule:

a + 0 = a

= \frac{1}{2}